Given Data Summary
| Action | S1 | S2 | S3 | S4 |
|---|---|---|---|---|
| A1 | 20 | 28 | 45 | 39 |
| A2 | 29 | 25 | 28 | 36 |
| A3 | 62 | 58 | 48 | 59 |
| A4 | 52 | 56 | 48 | 51 |
Probabilities:
-
S1: 0.30
-
S2: 0.22
-
S3: 0.18
-
S4: 0.30
a) Maximax Criterion
-
Choose the action with the maximum of the maximum payoffs.
-
Max Payoffs:
-
A1: 45
-
A2: 36
-
A3: 62
-
A4: 56
-
-
✅ Optimum Action (Maximax): A3
b) Laplace Criterion - average
- Assumes all states are equally likely.
- Choose action with the highest average payoff.
| Action | Average Payoff |
|---|---|
| A1 | 33.00 |
| A2 | 29.50 |
| A3 | 56.75 |
| A4 | 51.75 |
- ✅ Optimum Action (Laplace): A3
c) EOL Criterion (Expected Opportunity Loss)
EOL Values:
| Action | EOL |
|---|---|
| A1 | 25.74 |
| A2 | 27.66 |
| A3 | 0.00 |
| A4 | 5.84 |
- ✅ Optimum Action (EOL): A3
EVPI (Expected Value of Perfect Information)
-
Best Payoff per State:
-
S1: 62 (A3)
-
S2: 58 (A3)
-
S3: 48 (A3, A4)
-
S4: 59 (A3)
-
-
EVwPI:
(62×0.30)+(58×0.22)+(48×0.18)+(59×0.30)=57.7(62×0.30) + (58×0.22) + (48×0.18) + (59×0.30) = 57.7
-
Best EMV among all actions:
- A3 has the highest EMV = 57.7
-
EVPI = EVwPI - Best EMV
EVPI=57.7−57.7=0EVPI = 57.7 - 57.7 = 0
- ✅ EVPI = 0, which means perfect information offers no additional value (because one action — A3 — dominates all states).
✅ Final Recommendations
-
Best Action under all criteria: A3
-
EVPI = 0 → No benefit from perfect information
Let me know if you’d like this formatted for handwritten notes or with step-by-step calculations.